A spherical ball of lead, 3 cm in diameter is melted and recast into…

Question

A spherical ball of lead, 3 cm in diameter is melted and recast into three spherical ball. The diameter of two of these are 1.5 cm and 2 cm respectively. The diameter of the third ball is :

Accepted Answer

Option A. 2.5 cm. Answer & Solution Answer: Option A Solution: Let the radius of the third ball be R cm Then, 4/3 × ( 3/4 )^3 + 4/3 × ( 1 )^3 + 4/3 × R^3 = 4/3 × ( 3/2 )^3 & 2764 + 1 + R^3 = 278 & R^3 = 12564 = ( 5 )^3 ( 4 )^3 & R = 5/4 ∴ Diameter of the third ball : = 2R = 5/2cm = 2.5\,cm